The rallies on Saturday, which drew 8,000 people according to police estimates, ended peacefully although there was palpable tension at times.

Image:A trio of nationalist groups of around 4,500 members held rallies in the city

Under German Chancellor Angela Merkel’s immigration policy, more than one million migrants and refugees have been allowed into Germany since 2015.

Around 4,500 far-right supporters from various movements including the far-right anti-immigration alternative for Germany (AfD) party and the anti-Islam PEGIDA movement attended, according to police.

The far-right protesters marched holding large portraits of victims of attacks by what they claim are asylum seekers.

Some chanted “Merkel must go” and “We are the people” while waving German flags.

Image:Some 3,500 marched in support of Mrs Merkel’s immigrant policy

Some 3,500 marched in support of Mrs Merkel’s policy, carrying banners reading “Chemnitz is neither grey nor brown” and “Heart instead of hate”.

Foreign Minister Heiko Maas tweeted in support of those marching against the far-right supporters: “The Second World War started 79 years ago. Germany caused unimaginable suffering in Europe. If once again people are parading today in the streets making Nazi salutes, our past history forces us to resolutely defend democracy.”

Image:Some of the far-right supporters chanted ‘Merkel must go’ and ‘We are the people’

One of the Greens’ leaders, Cem Ozdemir, tweeted a picture of himself with demonstrators and wrote: “We will not let right-wing extremists destroy our country and our democracy. Neither in Chemnitz, nor in Saxony nor anywhere in Germany.

“Our constitution must prevail. We must defend it. Now!”

There was a heavy police presence in the city, with forces from across Germany providing reinforcements.

They had been outnumbered by thousands of neo-Nazis and other extremists earlier this week.

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The violence has applied renewed pressure on Mrs Merkel’s most divisive political issue.

Her government has increasingly restricted the once generous asylum laws, as conservative and far-right disquiet has grown.